I do not understand why the torsion is set equal to zero in the general theory of relativity. The geodesics would be the same. Is there even a way to test it?
Pg 250 from the 2017 edition of MTW says
$\nabla$ is said to be a "symmetric" or "torsion-free" covariant derivative when $\nabla_{\mathbf{u}}\mathbf{v}-\nabla_{\mathbf{v}}\mathbf{u} = [\mathbf{u}, \mathbf{v}]$. Other types of covariant derivatives, as studied by mathematicians, have no relevance for any gravitation theory based on the equivalence principle.
but I don't know what does this have to do with the equivalence principle.
